Question

protein grams in fast food the amount of protein (in grams) in a variety of fast - food sandwiches is represented in the frequency distribution shown here. construct a relative frequency polygon for the data.
class limits frequency
15 - 19 4
20 - 24 6
25 - 29 9
30 - 34 8
35 - 39 5
40 - 44 2
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part 1 of 2
construct a relative frequency distribution. round your answers to three decimal places, if necessary.
class limits midpoints relative frequency
15 - 19 17 0.125
20 - 24 22 0.188
25 - 29 27 0.281
30 - 34 32 0.250
35 - 39 37 0.094
40 - 44 42 0.063

Explanation:

Step1: Calculate total frequency

First, we need to find the total number of observations (total frequency). We sum up all the frequencies: \(4 + 6 + 9 + 8 + 5 + 2\)
\(4+6 = 10\), \(10 + 9 = 19\), \(19 + 8 = 27\), \(27 + 5 = 32\), \(32 + 2 = 34\). So total frequency \(N = 34\).

Step2: Calculate relative frequency for each class

Relative frequency is calculated as \(\text{Relative Frequency} = \frac{\text{Frequency of the class}}{N}\)

• For class \(15 - 19\): Frequency \(f = 4\), so relative frequency \(=\frac{4}{34}\approx0.118\) (rounded to three decimal places)
• For class \(20 - 24\): Frequency \(f = 6\), so relative frequency \(=\frac{6}{34}\approx0.176\) (rounded to three decimal places)
• For class \(25 - 29\): Frequency \(f = 9\), so relative frequency \(=\frac{9}{34}\approx0.265\) (rounded to three decimal places)
• For class \(30 - 34\): Frequency \(f = 8\), so relative frequency \(=\frac{8}{34}\approx0.235\) (rounded to three decimal places)
• For class \(35 - 39\): Frequency \(f = 5\), so relative frequency \(=\frac{5}{34}\approx0.147\) (rounded to three decimal places)
• For class \(40 - 44\): Frequency \(f = 2\), so relative frequency \(=\frac{2}{34}\approx0.059\) (rounded to three decimal places)

Answer:

Class limits	Midpoints	Relative frequency
20 - 24	22	0.176
25 - 29	27	0.265
30 - 34	32	0.235
35 - 39	37	0.147
40 - 44	42	0.059